SOLUTION: A cube is 8 inches on each side. What is the height of a cylinder having the same volume, if its radius is 4 inches?

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Question 587207: A cube is 8 inches on each side. What is the height of a cylinder having the same volume, if its radius is 4 inches?
Answer by Schaman_Dempster(26) About Me  (Show Source):
You can put this solution on YOUR website!
We know that side length of a cube is 8 inches.
Volume of the cube = +%28side+length%29%5E3+
V(cube) = +8%5E3+
V(cube) = 512 cubic inches
WE know that the radius of the cylinder is r = 4 inches and let the height of the cylinder be h inches.
Volume of the cylinder = π+r%5E2%2Ah+
V(cylinder) = +pi%2A4%5E2%2Ah+
V(cylinder) = 16πh
Since the volume of cube and cylinder are same, so
V(cylinder) = V(cube)
or 16πh = 512
or πh = 512/16 {Dividing both the sides by 16}
or πh = 32
or h = 32/π inches
If we wish to get the decimal value fo h, we can use the standard value of π = 3.14
Therefore, h = 32/π = 32/3.14
or h = 10.189
or h = 10.2 inches (approximately)


Hope this helps~!